Field of the Invention
The present invention relates to methods and apparatus for measuring a structure on a substrate. The invention can be applied for example in model based metrology of microscopic structures, for example to assess critical dimensions (CD) or overlay performance of a lithographic apparatus.
Related Art
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, can be used to generate a circuit pattern be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., comprising part of, one, or several dies) on a substrate (e.g., a silicon wafer).—Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In order to monitor the lithographic process, parameters of the patterned substrate are measured. Parameters can include, for example, the overlay error between successive layers formed in or on the patterned substrate and critical linewidth of developed photosensitive resist. This measurement can be performed on a product substrate and/or on a dedicated metrology target. There are various techniques for making measurements of the microscopic structures formed in lithographic processes, including the use of scanning electron microscopes and various specialized tools. A fast and non-invasive form of specialized inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered or reflected beam are measured. Two main types of scatterometer are known. Spectroscopic scatterometers direct a broadband radiation beam onto the substrate and measure the spectrum (intensity as a function of wavelength) of the radiation scattered into a particular narrow angular range. Angularly resolved scatterometers use a monochromatic radiation beam and measure the intensity of the scattered radiation as a function of angle.
By comparing the properties of the beam before and after it has been reflected or scattered by the substrate, the properties of the substrate can be determined. This can be done, for example, by comparing data obtained from measurement of the reflected or scattered beam with model, e.g., simulated, diffraction signals calculated from a parameterized model. The calculated signals can be pre-calculated and stored in a library, the library representing a plurality of candidate substrate structures distributed in a parameter space of the parameterized model. Alternatively or in addition, parameters can be varied during an iterative search process, until a calculated diffraction signal matches the measured signal. In U.S. Pat. No. 7,522,293 to Wu et al., for example, these two techniques are described for example as ‘library based’ and ‘regression based’ processes, respectively.
In particular for complex structures, or structures including particular materials, the number of parameters required to model the scattered beam accurately is high. A ‘model recipe’ can be defined in which parameters are defined as either given, e.g., fixed, or variable, e.g., floating. For floating parameters, the permitted range of variation is defined, either in absolute terms or by reference to deviation from a nominal value. Each floating parameter in the recipe represents another degree of freedom in the model, and consequently another dimension in the multidimensional parameter space in which the best matching candidate structure is to be found. Even with a handful of parameters, the size of computational tasks quickly becomes very large, for example by raising the number of library samples unacceptably. It also raises the risk of falsely matching parameter sets that do not correspond to the measured substrate. Unfortunately, fixing a parameter to a value that is not identical to what is in the measured structure will distort the matching process so that inaccuracy arises in floating parameters, which can be the parameters of most interest. The recipe is therefore a delicate compromise between accuracy and practicality of computation.